Data decompression with extra precision

ABSTRACT

Methods and systems for decompressing data are described. The relative magnitudes of a first value and a second value are compared. The first value and the second value represent respective endpoints of a range of values. The first value and the second value each have N bits of precision. Either the first or second value is selected, based on the result of the comparison. The selected value is scaled to produce a third value having N+1 bits of precision. A specified bit value is appended as the least significant bit of the other (non-selected) value to produce a fourth value having N+1 bits of precision.

RELATED UNITED STATES PATENT APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 10/990,884 by D. Rogers et al., filed on Nov. 16,2004, entitled “Data Compression with Extra Precision,” now U.S. Pat.No. 8,078,656, assigned to the assignee of the present invention, andhereby incorporated by reference in its entirety.

This application is related to U.S. patent application Ser. No.10/990,900 by D. Rogers et al., filed on Nov. 16, 2004, entitled “TwoComponent Texture Map Compression,” now U.S. Pat. No. 7,961,195,assigned to the assignee of the present invention, and herebyincorporated by reference in its entirety.

FIELD OF THE INVENTION

Embodiments of the present invention generally relate to datadecompression, in particular data used in connection with computergraphics.

BACKGROUND ART

As a result of continuing advances in computer graphics, images thatlook more and more realistic are being rendered in applications such asvideo games. A key to achieving a convincing image is the ability torealistically simulate lighting and shadowing effects on a textured(e.g., three-dimensional) surface.

One technique for rendering surface textures involves the use of normalmaps. When rendering using normal maps, each point on a surface to berendered is associated with a unit length vector that is perpendicularto that point. The normal vector indicates the direction that thesurface is facing at that point. Using a normal map, contemporarygraphics engines can render very complex looking surfaces to achieve amore realistic effect.

A normal map can contain a large quantity of data, especially whenrealistic-looking surfaces at high screen (display) resolutions arebeing portrayed. Compression schemes are usually employed to reduce theamount of data. However, conventional real-time compression techniquescan result in a loss of precision when the data are reconstructed,leading to reduced image quality.

SUMMARY OF THE INVENTION

Accordingly, a system and/or method that can reconstruct compressednormals with improved precision would be advantageous. Embodiments inaccordance with the present invention provide this and other advantages.

In one embodiment of the present invention, the relative magnitudes of afirst value and a second value are compared. The first value and thesecond value represent respective endpoints of a range of values. Thefirst value and the second value each have N bits of precision. Eitherthe first or second value is selected, based on the result of thecomparison. The selected value is scaled to produce a third value havingN+1 bits of precision. A specified bit value is appended as the leastsignificant bit of the other (non-selected) value to produce a fourthvalue having N+1 bits of precision. Intermediate values can then bedetermined by interpolating between the third and fourth values.

In one embodiment, the third and fourth values are nine (9) bits inlength (that is, N+1 is 9). In one such embodiment, the first and secondvalues are signed values normalized to the range of [−1, 1] coded ineight (8) bits each (e.g., one byte), the 8 bits having a value in therange of [−127, 127]. In another such embodiment, the first and secondvalues are unsigned values coded in 8 bits each, the 8 bits having avalue in the range of [0, 255].

In one embodiment, the data being decompressed include texel data usedin connection with computer graphics systems. In such an embodiment, thethird and fourth values of N+1 bits (and the first and second values ofN bits) correspond to one component (e.g., the x-component or they-component, etc.) of a texel at a location in a block of data. However,the decompression method described above can be applied to any number ofcomponents in other types of applications.

In summary, embodiments of the present invention provide methods andsystems for decompressing data with improved precision. As a result, thequality of rendered images can be increased. Importantly, theimprovement in precision is achieved without actually storing extra bitsof precision in a block of compressed data. In effect, the extra bits ofprecision are “virtual” bits that are not stored in the compressionblock, but instead are derived from other information in the compressionblock. Thus, improved precision is achieved without significantlyincreasing the burden on computational resources and without increasingthe size or changing the structure of the compression block. These andother objects and advantages of the various embodiments of the presentinvention will be recognized by those of ordinary skill in the art afterreading the following detailed description of the embodiments that areillustrated in the various drawing figures.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and form a part ofthis specification, illustrate embodiments of the present invention and,together with the description, serve to explain the principles of theinvention:

FIG. 1 is a block diagram of an exemplary computer system upon whichembodiments of the present invention can be implemented.

FIG. 2 is a block diagram showing the flow of data into and out of adata encoder, and into and out of a data decoder, according to oneembodiment of the present invention.

FIG. 3 illustrates a palette that includes anchor endpoints and otherpoints derived from the endpoints according to one embodiment of thepresent invention.

FIG. 4 is a data flow diagram showing a manner in which a palette can beused to encode data according to one embodiment of the presentinvention.

FIG. 5 illustrates a memory-resident block of compressed data accordingto one embodiment of the present invention.

FIG. 6 is a flowchart of an exemplary computer-implemented method fordecompressing data in accordance with one embodiment of the presentinvention.

The drawings referred to in the description should not be understood asbeing drawn to scale except if specifically noted.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to the various embodiments of thepresent invention, examples of which are illustrated in the accompanyingdrawings. While the invention will be described in conjunction withthese embodiments, it will be understood that they are not intended tolimit the invention to these embodiments. On the contrary, the inventionis intended to cover alternatives, modifications and equivalents, whichmay be included within the spirit and scope of the invention as definedby the appended claims. Furthermore, in the following detaileddescription of the present invention, numerous specific details are setforth in order to provide a thorough understanding of the presentinvention. However, it will be understood that the present invention maybe practiced without these specific details. In other instances,well-known methods, procedures, components, and circuits have not beendescribed in detail so as not to unnecessarily obscure aspects of thepresent invention.

Some portions of the detailed descriptions that follow are presented interms of procedures, logic blocks, processing, and other symbolicrepresentations of operations on data bits within a computer memory.These descriptions and representations are the means used by thoseskilled in the data processing arts to most effectively convey thesubstance of their work to others skilled in the art. In the presentapplication, a procedure, logic block, process, or the like, isconceived to be a self-consistent sequence of steps or instructionsleading to a desired result. The steps are those utilizing physicalmanipulations of physical quantities. Usually, although not necessarily,these quantities take the form of electrical or magnetic signals capableof being stored, transferred, combined, compared, and otherwisemanipulated in a computer system. It has proven convenient at times,principally for reasons of common usage, to refer to these signals astransactions, bits, values, elements, symbols, characters, fragments,pixels, or the like.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise as apparent from the followingdiscussions, it is appreciated that throughout the present invention,discussions utilizing terms such as “comparing,” “storing,” “using,”“compressing,” “decompressing,” “restoring,” “determining,”“constructing,” “producing,” “accessing,” “calculating,” “selecting,”“associating,” “truncating,” “scaling,” “appending” or the like, referto actions and processes (e.g., flowchart 60 of FIG. 6) of a computersystem or similar electronic computing device. The computer system orsimilar electronic computing device manipulates and transforms datarepresented as physical (electronic) quantities within the computersystem memories, registers or other such information storage,transmission or display devices. The present invention is well suited touse with other computer systems.

FIG. 1 is a block diagram of an exemplary computer system 112 upon whichembodiments of the present invention can be implemented. Computer system112 includes an address/data bus 100 for communicating information, acentral processor 101 coupled with bus 100 for processing informationand instructions; a volatile memory unit 102 (e.g., random access memory[RAM], static RAM, dynamic RAM, etc.) coupled with bus 100 for storinginformation and instructions for central processor 101; and anon-volatile memory unit 103 (e.g., read only memory [ROM], programmableROM, flash memory, etc.) coupled with bus 100 for storing staticinformation and instructions for processor 101. Computer system 112 alsoincludes a display device 105 coupled to bus 100 for displayinginformation to the computer user. Moreover, computer system 112 alsoincludes a data storage device 104 (e.g., disk drive) for storinginformation and instructions.

Also included in computer system 112 is an optional alphanumeric inputdevice 106. Device 106 can communicate information and commandselections to central processor 101. Computer system 112 also includes acursor control or directing device 107 coupled to bus 100 forcommunicating user input information and command selections to centralprocessor 101. Computer system 112 also includes signal communicationinterface (input/output device) 108, which is also coupled to bus 100.Communication interface 108 can also include wireless communicationmechanisms.

It is appreciated that computer system 112 described herein illustratesan exemplary configuration of an operational platform. Nevertheless,other computer systems with differing configurations can also be used inplace of computer system 112 within the scope of the present invention.These other types of computer systems can include workstations and thinclient devices that are coupled to other computer systems in adistributed computer system network. Computer system 112 may be any typeof computing device, such as but not limited to a personal computer, agame console, a personal digital assistant, a cell phone, a portabledigital device, etc.

FIG. 2 is a block diagram showing the flow of data into and out of adata encoder 22, and into and out of a data decoder 24, according to oneembodiment of the present invention. Encoder 22 compresses the data 21using an encoding scheme that is described more fully in conjunctionwith FIGS. 3 and 4 and Table 1. In overview, encoder 22 selects anchorpoints or endpoints that bound the range of values of the data 21. Theanchor points are used to generate a palette (e.g., a lookup table)containing values that lie between the anchor points. A unique index orbit code is associated with each of the anchor points and with each ofthe intermediate values. The bit codes can be used to encode each of thevalues in data 21 to generate the compressed data 23. In essence, eachof the values in data 21 is replaced with a bit code that is shorter inlength. For example, integer values zero (0) through seven (7), a totalof eight values, can each be encoded as a bit code that is three bits inlength.

The compression block includes the two anchor points and the encoded bitcodes. Thus, compressed data 23 includes fewer bits than are included indata 21. Decoder 24 of FIG. 2 decompresses (reconstructs) the compresseddata 23 to generate the reconstructed data 25. In general, the anchorpoints are used to reconstruct the palette. The palette is used with theencoded bit codes to construct a decompressed version of the originaldata. Additional information is provided in conjunction with FIGS. 5 and6 and Tables 2, 3, 4 and 5, below.

FIG. 3 illustrates a palette that includes anchor endpoints and otherpoints derived from the endpoints according to one embodiment of thepresent invention. The use of a palette for encoding data is describedfurther in conjunction with FIG. 4 below.

With reference to FIG. 3, in the present embodiment, two anchor points(P0 and P1) are defined. The remaining points P2 through P7 are derivedusing percentages of P0 and P1.

In general, the points P0 and P1 are each represented using N+1 bits andencoded using N bits. In one embodiment, the points P0 and P1 are eachrepresented using nine (9) bits and encoded (compressed) using eight (8)bits each. In one embodiment, this is accomplished by truncating theleast significant bit from each of P0 and P1.

Six other points (P2, P3, P4, P5, P6 and P7) are linearly interpolatedusing P0 and P1, yielding a total of 8 values for the palette. Each ofthe points P0 through P7 is associated with a unique bit code (refer tothe discussion of FIG. 4 below).

Table 1 provides one example of code that can be used to generate apalette according to one embodiment of the present invention.

TABLE 1 Exemplary Code for Generating a Palette  P0 = // bit code 000 P1 = // bit code 001  P2 = (6 * P0 + 1 * P1) / 7; // bit code 010  P3 =(5 * P0 + 2 * P1) / 7; // bit code 011  P4 = (4 * P0 + 3 * P1) / 7; //bit code 100  P5 = (3 * P0 + 4 * P1) / 7; // bit code 101  P6 = (2 *P0 + 5 * P1) / 7; // bit code 110  P7 = (1 * P0 + 6 * P1) / 7; // bitcode 111 }

According to the various embodiments of the present invention, P0 and P1are either signed values or unsigned values. Signed values arenormalized to the range [−1, 1] and the interpolation scheme describedabove (Table 1) is used, except the values for P0 and P1 are signed andthe results are not clamped to integer values.

The present invention will be described for an embodiment in which thedata to be compressed (encoded) are associated with a single component.Although described in the context of a single component, embodiments inaccordance with the present invention are not so limited. Embodiments ofthe present invention can also be applied to other types ofmultiple-element, unconstrained or arbitrary data such as sphericalharmonic data, by applying multiples of the elements of thecompression/decompression scheme described herein (that is, by applyingthe scheme described herein to each component when there are multiplecomponents).

FIG. 4 illustrates how a palette 44 can be used to encode data accordingto one embodiment of the present invention. Palette 44 is amemory-resident data structure and includes the anchor points P0 and P1and the intermediate range of values P2 through P7 that wereinterpolated using P0 and P1. Each of the values P0 through P7 isindexed by a respective and unique bit code. In the present embodiment,the bit code uses three (3) bits.

In the example of FIG. 4, the x-component (X1, X2, . . . , X15, X16) ofthe normal vector associated with each texel in a memory-resident blockof texels 42 is to be encoded. The x-component example can be extendedreadily to other components of normal vectors (e.g., the y-component),or other types of components used in other types of coordinate orreference systems. That is, as mentioned above, the present invention isnot limited in application to only a single component, nor is thepresent invention limited to the components of normal vectors. Also,although the block of texels 42 includes 16 texels, the presentinvention is not so limited.

In the present embodiment, during the compression phase, the x-componentvalues X1 through X16 are each compared to the values P0 through P7, inorder to determine which of the values in the palette 44 eachx-component value is closest to. For instance, if the value X1 iscompared to the values P0 through P7 and found to be closest to thevalue P0, then bit code 000 would be associated with X1. Similarly, ifX5 is found to be closest to P2, then bit code 010 would be associatedwith X5. In general, each of the data values in the block of texels 42is associated with a bit code selected from palette 44. As a result, amemory-resident encoded block of texels 46 includes an exemplary bitcode or index for each of the values in block of texels 42.

FIG. 5 illustrates memory-resident compression block 50 according to oneembodiment of the present invention. As can be seen, portion 55 actuallyincludes a plurality of portions, each portion holding or storing a bitcode for each x-component in the block of texels 42 (FIG. 4).

In the example of FIG. 5, compression block 50 includes a first portion51 for holding or storing a first encoded value (e.g., P0), a secondportion 52 for holding or storing a second encoded value (e.g., P1), anda portion 55 for holding or storing selected bit codes (e.g., the bitcodes selected from palette 44 of FIG. 4). In one embodiment, each ofthe bit codes in portion 55 is 3 bits in length. In one embodiment, theportions 51 and 52 are each 8 bits in length.

As mentioned above, in one embodiment, the endpoints P0 and P1 are eachrepresented using N+1 (e.g., 9) bits before they are encoded as N-bit(e.g., 8-bit) strings. In other words, in general, P0 and P1 are eachreduced from N+1 bits to N bits before they are stored in compressionblock 50. In one embodiment, this is accomplished by truncating theleast significant bit from each of P0 and P1.

Compression block 50 is decompressed by decoder 24 of FIG. 2. Asmentioned above, the data represented by compression block 50 may beeither signed or unsigned.

Table 2 provides one example of code used for unsigned decompression inaccordance with the present invention.

TABLE 2 Exemplary Code for Unsigned Decompression if P0>P1  P1=(P1<<1)|1; //shift P1 left by 1 and set the least significant   bit(lsb) to 1   unsigned scale P0 to 9 bits else   P0=(P0<<1)|0; //shift P0left by 1 and set lsb to 0   unsigned scale P1 to 9 bits

One example of the “unsigned scale operation” mentioned in Table 2 isprovided in Table 3.

TABLE 3 Exemplary Code for Unsigned Scale Operation out=(in<<1)|(in>>7)//shift the input (P0 or P1) left by 1 and shift the input (P0 or P1)right by 7, and concatenate the two pieces to get a 9-bit output (P0 orP1)

The exemplary code of Table 3 is a fixed point operation equivalent tothe floating point operation given by:out=(int)floor(in*511.0/255.0+0.5).

Scaling by 511/255 is being done so that 8 bits are scaled to 9 bitssuch that values in the range [0 . . . 255] map as evenly as possible tothe range [0 . . . 512]. Similarly, for signed values, the signed range[−127 . . . 127] is mapped as evenly as possible to the signed range[−255 . . . 255], as described below.

Table 4 provides one example of code used for signed decompression inaccordance with the present invention.

TABLE 4 Exemplary Code for Signed Decompression if abs(P0)>abs(P1)//”abs” refers to the absolute value   P1=(P1<<1)|1; //shift P1 left by1 and set lsb to 1   signed scale P0 to 9 bits else   P0=(P0<<1)|0;//shift P0 left by 1 and set lsb to 0   signed scale P1 to 9 bits

One example of the “signed scale operation” mentioned in Table 4 isprovided in Table 5.

TABLE 5 Exemplary Code for Signed Scale Operationout=(in==−128)?−256:((in<0)?−(((−in)<<1)|((−in)>>6)):((in<<1)|(in>>6)))//where “in” and “out” are either P0 or P1

The exemplary code of Table 5 is a fixed point operation equivalent tothe floating point operation given by:out=(in==−128)?−256:(int)floor(1*255.0/127.0+0.5).

The decompressed 9-bit P0 and P1 values are used in the interpolation ofTable 1 to construct the palette values. Note that although thedecompressed P0 and P1 are 9-bit values, the palette values are notlimited to 9 bits of precision. That is, the values interpolated from P0and P1 can be greater than 9 bits in length.

FIG. 6 is a flowchart 60 of a computer-implemented method fordecompressing data in accordance with one embodiment of the presentinvention. Although specific steps are disclosed in flowchart 60, suchsteps are exemplary. That is, the present invention is well suited toperforming various other steps or variations of the steps recited inflowchart 60. It is appreciated that the steps in flowchart 60 may beperformed in an order different than presented and that the steps inflowchart 60 are not necessarily performed in the sequence illustrated.In one embodiment, flowchart 60 is implemented as program instructionsstored in computer-readable memory units of computer system 112 andexecuted by processor 101 (FIG. 1). In the present embodiment, flowchart60 provides a general description of the operations described by Tables2, 3, 4 and 5.

In step 62 of FIG. 6, in the present embodiment, the relative magnitudesof a first value and a second value in a memory-resident compressionblock are compared (see Tables 2 and 4). The first value and the secondvalue represent respective endpoints of a range of values, and each haveN bits of precision. With reference to FIG. 5, in one embodiment, themagnitude of a value in portion 51 of compression block 50 is comparedto the magnitude of a value in portion 52. The first and second valuesmay be signed or unsigned. If the values are signed, the absolute valuesof the first and second values are compared.

In step 64 of FIG. 6, depending on the results of the comparison, eitherthe first value or the second value is identified as being the valuethat is larger in magnitude (see Tables 2 and 4).

In step 66, in one embodiment, the value identified in step 64 is scaledto produce a third value that has N+1 bits of precision. That is, in oneembodiment, the value that has the larger magnitude is scaled using ascaling operation. In one embodiment, the value is scaled using one ofthe scaling operations described by Tables 3 and 5.

In step 68, in one embodiment, a specified bit value (e.g., either 0or 1) is appended as the least significant bit (lsb) to the other value(e.g., the value that has the smaller magnitude) to produce a fourthvalue that has N+1 bits of precision. As shown by Tables 2 and 4, thespecified bit value depends on which of the first and second values isidentified in step 64 as having the larger magnitude. Looking at Table2, for example, if P0 has the greater magnitude, then a value of 1 isappended to P1 as the least significant bit of P1, while if P1 has thegreater magnitude, then a value of 0 is appended to P0 as the leastsignificant bit of P0.

The third and fourth values determined according to flowchart 60 canthen be used to interpolate a range of other values, for example toreconstruct a palette as described previously herein.

In summary, embodiments of the present invention provide methods andsystems for compressing and reconstructing data with improved precision.As a result, the quality of rendered images can be increased. Theimprovement in precision is achieved without actually storing extraprecision bits. In effect, the extra precision bits are “virtual” bitsthat are not stored in the compression block, but whose values arederived from other information that is stored in the compression block.Thus, improved precision is achieved without significantly increasingthe burden on computational resources and without increasing the size orchanging the structure (format) of the compression block.

Embodiments of the present invention, data decompression with extraprecision, are thus described. While the present invention has beendescribed in particular embodiments, it should be appreciated that thepresent invention should not be construed as limited by suchembodiments, but rather construed according to the below claims.

What is claimed is:
 1. A computer system comprising: a processor; and amemory unit coupled to said processor, said memory unit havingcomputer-readable program instructions stored therein that when executedcause said computer system to implement a method for processing data,said method comprising said computer system: comparing the magnitude ofa first value and the magnitude of a second value in a compression blockresident in said memory unit, wherein said first and second values arestored in a particular order relative to one another in said compressionblock, said first value and said second value representing respectiveendpoints of a range of values, said first value and said second valueeach having N bits; selecting one of said first and second valuesaccording to the result of said comparing, thereby yielding a selectedvalue that is one of said first and second values and an unselectedvalue that is the other of said first and second values; scaling saidselected value to produce a third value representing a decompressedvalue of said selected value and having N+1 bits of precision; usingsaid particular order in which said first and second values are storedin said compression block to derive a specified one-bit value, whereinsaid specified one-bit value has one binary value if said first value isstored before said second value in said compression block and otherwisesaid specified one-bit value has the other binary value, wherein saidspecified one-bit value is appended to said unselected value as theleast significant bit of said unselected value to produce a fourth valuerepresenting a decompressed value of said unselected value and havingN+1 bits of precision; and interpolating values that have N+1 bits ofprecision using said third and fourth values.
 2. The computer system ofclaim 1 wherein said selected value has a larger magnitude than saidunselected value.
 3. The computer system of claim 1 wherein said firstand second values are signed values normalized to the range of [−1, 1]coded in eight (8) bits each, said 8 bits having a value in the range of[−127, 127].
 4. The computer system of claim 3 wherein said comparing ofsaid method uses the absolute values of said first and second values. 5.The computer system of claim 1 wherein said first and second values areunsigned values coded in 8 bits each, said 8 bits having a value in therange of [0, 255].
 6. The computer system of claim 1 wherein said datacomprise data for a normal map used in graphics processing.
 7. Anon-transitory computer-readable storage unit having programinstructions stored therein for causing a computer system to perform amethod comprising: comparing the magnitude of a first value and themagnitude of a second value in a memory-resident compression block,wherein said first and second values are stored in a particular orderrelative to one another in said compression block, said first value andsaid second value representing respective endpoints of a range ofvalues, said first value and said second value each having N bits;selecting one of said first and second values according to the result ofsaid comparing, thereby yielding a selected value that is one of saidfirst and second values and an unselected value that is the other ofsaid first and second values; scaling said selected value to produce athird value representing a decompressed value of said selected value andhaving N+1 bits of precision; and using said particular order in whichsaid first and second values are stored in said compression block toderive a specified single bit value, wherein said specified single bitvalue has one binary value if said first value is stored in a positionin said compression block that is read before said second value andotherwise said single bit value has the other binary value, wherein saidsingle bit value is appended to said unselected value as the leastsignificant bit of said unselected value to produce a fourth valuerepresenting a decompressed value of said unselected value and havingN+1 bits of precision.
 8. The non-transitory computer-readable unit ofclaim 7 wherein said selected value has a larger magnitude than saidunselected value.
 9. The non-transitory computer-readable storage unitof claim 7 wherein said first and second values are signed valuesnormalized to the range of [−1, 1] coded in eight (8) bits each, said 8bits having a value in the range of [−127, 127].
 10. The non-transitorycomputer-readable storage unit of claim 9 wherein said comparing usesthe absolute values of said first and second values.
 11. Thenon-transitory computer-readable storage unit of claim 7 wherein saidfirst and second values are unsigned values coded in 8 bits each, said 8bits having a value in the range of [0, 255].
 12. The non-transitorycomputer-readable storage unit of claim 7 wherein said range of valuescomprise data for a normal map used in graphics processing.
 13. In acomputer system comprising a processor and a memory unit, a method forprocessing data implemented by said computer system, said methodcomprising: comparing the magnitude of a first value and the magnitudeof a second value in a compression block resident in said memory unit,wherein said first and second values are stored in a particular orderrelative to one another in said compression block, said first value andsaid second value representing respective endpoints of a range ofvalues, said first value and said second value each having N bits;selecting one of said first and second values according to the result ofsaid comparing, thereby yielding a selected value that is one of saidfirst and second values and an unselected value that is the other ofsaid first and second values; scaling said selected value to produce athird value representing a decompressed value of said selected value andhaving N+1 bits of precision; using said particular order in which saidfirst and second values are stored in said compression block to derive aspecified one-bit value, wherein said specified one-bit value has onebinary value if said first value is stored before said second value insaid compression block and otherwise said specified one-bit value hasthe other binary value, wherein said specified one-bit value is appendedto said unselected value as the least significant bit of said unselectedvalue to produce a fourth value representing a decompressed value ofsaid unselected value and having N+1 bits of precision; andinterpolating values that have N+1 bits of precision using said thirdand fourth values.
 14. The method of claim 13 wherein said selectedvalue has a larger magnitude than said unselected value.
 15. The methodof claim 13 wherein said first and second values are signed valuesnormalized to the range of [−1, 1] coded in eight (8) bits each, said 8bits having a value in the range of [−127, 127].
 16. The method of claim15 wherein said comparing uses the absolute values of said first andsecond values.
 17. The method of claim 13 wherein said first and secondvalues are unsigned values coded in 8 bits each, said 8 bits having avalue in the range of [0, 255].
 18. The method of claim 13 wherein saiddata comprise data for a normal map used in graphics processing.